Screen LibraryThe collected papers of Stephen Smale. Volume 2 /
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains...
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| Group Author: | ; |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 2000. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/4424-vol2#t=toc |
| Summary: |
This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views. |
| Carrier Form: | 1 online resource (xi,[540]pages) : illustrations |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9789812792822 |
| CLC: | O1-53 |
| Contents: | pt. IV. Calculus of variations (global analysis) and PDE's. Smale and nonlinear analysis: A personal perspective / A. J. Tromba -- A generalized Morse theory / R. Palais -- Morse theory and a non-linear generalization of the Dirichlet problem -- On the calculus of variations -- An infinite dimensional version of Sard's theorem -- On the Morse index theorem -- correction to "On the Morse index theorem" -- What is global analysis? -- Book review on "Global variational analysis: Weierstrass integrals on a Riemannian manifold" by Marston Morse -- Smooth solutions of the heat and wave equations -- pt. V. Dynamics. On the contribution of smale to dynamical systems / J. Palis -- Discussion (S. Newhouse, R. F. Williams and others) -- Morse inequalities for a dynamical system -- On dynamical systems -- Dynamical systems and the topological conjugacy problem for diffeomorphisms -- Stable manifolds for differential equations and diffeomorphisms -- A structurally stable differentiable homeomorphism with an infinite number of periodic points -- Diffeomorphisms with many periodic points -- Structurally stable systems are not dense -- Dynamical systems on n-dimensional manifolds -- Differentiable dynamical systems -- Nongenericity of [symbol]-stability / R. Abraham -- Structural stability theorems / J. Palis -- Notes on differential dynamical systems -- The [symbol]-stability theorem -- Stability and genericity in dynamical systems -- Beyond hyperbolicity / M. Shub -- Stability and isotopy in discrete dynamical systems -- Differential equations -- Dynamical systems and turbulence -- Review of "Catastrophe theory: selected papers, 1972-1977" by E. C. Zeeman -- On the problem of reviving the ergodic hypothesis of Boltzmann and Birkhoff -- On how I got started in dynamical systems -- Dynamics retrospective: Great problems, attempts that failed -- What is chaos? -- Finding a horseshoe on the beaches of Rio -- The work of Curtis T. McMullen -- pt. VI. Mechanics. Steve Smale and geometric mechanics / J. E. Marsden -- Topology and mechanics, I. -- Topology and mechanics, II. -- Problems on the nature of relative equilibria in celestial mechanics -- Personal perspectives on mathematics and mechanics -- pt. VII. Biology, electric circuits, mathematical programming. On the mathematical foundations of electrical circuit theory -- A mathematical model of two cells via Turing's equation -- Optimizing several functions -- Sufficient conditions for an optimum -- The qualitative analysis of a difference equation of population growth / R. F. Williams -- On the differential equations of species in competition -- The problem of the average speed of the simplex method -- On the average number of steps of the simplex method of linear programming. |